Problem: Takahashi loves sorting.

He has a permutation (p_1,p_2,...,p_N) of the integers from 1 through N. Now, he will repeat the following operation until the permutation becomes (1,2,...,N):

* First, we will define high and low elements in the permutation, as follows. The i-th element in the permutation is high if the maximum element between the 1-st and i-th elements, inclusive, is the i-th element itself, and otherwise the i-th element is low.
* Then, let a_1,a_2,...,a_k be the values of the high elements, and b_1,b_2,...,b_{N-k} be the values of the low elements in the current permutation, in the order they appear in it.
* Lastly, rearrange the permutation into (b_1,b_2,...,b_{N-k},a_1,a_2,...,a_k).



How many operations are necessary until the permutation is sorted?

Constraints

* 1 ≤ N ≤ 2×10^5
* (p_1,p_2,...,p_N) is a permutation of the integers from 1 through N.

Input

Input is given from Standard Input in the following format:


N
p_1 p_2 ... p_N


Output

Print the number of operations that are necessary until the permutation is sorted.

Examples

Input

5
3 5 1 2 4


Output

3


Input

5
5 4 3 2 1


Output

4


Input

10
2 10 5 7 3 6 4 9 8 1


Output

6

Solution (in CPP):

Solution:
//Heaplax
//别让自己后悔
#include<bits/stdc++.h>
#define N 200001
#define LL long long
#define LOG(x) cerr<<#x<<" = "<<x<<endl
#define add_edge(u,v) nxt[++cnt]=head[u],head[u]=cnt,to[cnt]=v
#define open(x) freopen(#x".in","r",stdin),freopen(#x".out","w",stdout)
char ch;bool fs;void re(int& x)
{
	while(ch=getchar(),ch<33);
	if(ch=='-')fs=1,x=0;else fs=0,x=ch-48;
	while(ch=getchar(),ch>33)x=x*10+ch-48;
	if(fs)x=-x;
}
using namespace std;
int n,p[N],q[N],T[N],f[N];
bool cyclic(int a,int b,int c)
{
	return (a<b&&b<c)||(b<c&&c<a)||(c<a&&a<b);
}
int main()
{
	re(n);
	for(int i=1;i<=n;++i)re(p[i]);
	for(int i=1;i<=n;++i)
		q[p[i]]=i;
	for(int i=n-1;i;--i)
	{
		if(!T[i+1])
		{
			if(q[i]<q[i+1])T[i]=0;
			else T[i]=1,f[i]=i+1;
		}
		else
		{
			if(cyclic(q[f[i+1]],q[i],q[i+1]))T[i]=T[i+1],f[i]=f[i+1];
			else T[i]=T[i+1]+1,f[i]=i+1;
		}
	}
	printf("%d\n",T[1]);
}